Abstract: Let G denote a connected reductive group over a nonarchimedean local field F.Let K denote a special maximal parahoric subgroup of GF. We establish aSatake isomorphism for the Hecke algebra H of K-bi-invariant compactlysupported functions on GF. The key ingredient is a Cartan decompositiondescribing the double coset space K\GF-K. We also describe how our resultsrelate to the treatment of Cartier, where K is replaced by a special maximalcompact open subgroup K- of GF and where a Satake isomorphism is establishedfor the Hecke algebra of K-bi-invariant compactly supported functions on GF.